The case \(p=n+1\)  is clear, because
then \(\Sigma (f)=X\) , the map is finite and \(\Delta (f)=f\) . We may thus
assume \(q\le n\) . Since \(f\)  is \(\) -finite, \(\Delta (f)\)  is an analytic
space of the same dimension as \(\Sigma (f)\) . On the one hand,
Sard's Theorem implies
that \(\Delta (f)\)  is not all of \(Z\) , hence its dimension is at
most \(p-1\) . On the other hand, \(\Sigma (f)\)  is defined as the vanishing
locus of \(p\) -minors of an \(n\times p\) -matrix with \(p \le n\) .
The results in [1]} imply that the dimension of
any component of \(\Delta (f)\)  is greater or equal to
\(n - (n - p + 1 ) = p-1\) .
